Use of Ridge and Principal Component Regression Analysis Methods in Multicollinearity

Ridge and principal component regression analysis methods are statistical analysis techniques that are used to analyze multiple regression data. in the case of multicollinearity, although least squares estimates are unbiased, variances of these estimates are larger and these variances can be farther than real values. with adding a degree of bias to regression estimates, standard errors of ridge and principal component regression are reduced. therefore, in the event of multicollinearity, ridge and principal component regression methods can be used as an alternative to least squares method. this investigation aimed to fit a model in order to estimate carcass weight from various body measurements of 91 cyprinus fish with different ages. as multicollinearity problems among body measurements were determined, ridge and principal component regression methods as an alternative to least squares method were applied for available data, performances of these three methods for the data were compared with each other. in order to compare effectiveness of these methods, coefficient of determination (r2), root of mean square error (rmse), mean square error (mse), and coefficient of variation as comparison criteria were used. according to these criteria, the best fit orders were observed in least squares (r2=0.905, s=19.587), ridge (r2=0.898, s=20.2563) and principal component regression (r2=0,878 s=22.127), respectively.as a result, it was concluded that, use of ridge and principal component regression analysis methods could be truer instead of least squares method under multicollinerity problem